

Direct Formula / Rule 11 :
Theorem:
A trader has N kg of a certain item, a part of
which he sells at x% profit and the rest at y% loss. On the
whole his loss is P%.
Then the quantity sold at x% profit is = 
( 
y  P 
) 
N Kg 
x + y 
and the quantity sold at y% loss is given by = 
( 
x + P 
) 
N Kg 
x + y 
Example :
A trader has 50 kg of rice, a part of which he sells at
14% profit and the rest at 6% loss. On the whole his
loss is 4%. What is the quantity sold at 14% profit
and that at 6% loss?
Detail Method :
Let the quantity sold at 14% profit be
x kg. Then the quantity sold at 6% loss will be (50  x)
kg.
For a matter of convenience suppose that the price of
rice is 1 rupee per kg.
Then price of x kg rice = Rs x and price of (50  x) kg
rice = Rs (50  x)
Now, we have
14% profit of x + 6% loss of (50  x)= 4% loss of 50
or, 14% of x  6% of (50  x) = 4% of 50
or, 14x 300 + 6x = 200
or, 20x = 100
∴ x = 5 kg
and 50  x = 50  5 = 45 kg.
Therefore, the quantity sold at 14% profit = 5 kg and
the quantity sold at 6% loss = 45 kg.
Ailigation Method :
(as there is loss on
the whole)
∴ ratio of quantities sold at 14% profit and 6% loss
= 2 : 18 = 1 : 9
∴ quantity sold at 14% profit = 
50 
X 1 = 5 kg, 
1 + 9 
and sold at 6% loss = 50  5 = 45 kg.
Note: Numbers in the third line should always be +ve. That
is why () 6  ()4 = 2 is not taken under consideration.
Quicker Method : Here you can use direct formula :
Quantity sold at 14% profit = 
( 
6  4 
) 
X 50 = 5 kg and 
14 + 6 
the quantity sold at 6% loss = 
( 
14 + 4 
) 
X 50 = 45 kg. 
14 + 6 
Exercise :

A trader has 40 kg of rice, a part of which he sells at 28%
profit and the rest at 12% loss. On the whole his loss is
8%. What is the quantity sold at 28% profit and that at
12% loss?

A trader has 48 kg of rice, a part of which he sells at 16%
profit and the rest at 8% loss. On the whole his loss is
6%. What is the quantity sold at 16% profit and that at
8% loss?

A trader has 44 kg of rice, a part o f which he sells at 26%
profit and the rest at 18% loss. On the whole his loss is
16%. What is the quantity sold at 26% profit and that at
18% loss?
Answers :
1 = 4 kg. 36 kg, 2 = 4 kg, 44 kg, 3 = 2 kg, 42 kg



